# Why is faithful actions called faithful and who first called it faithful?

I want to know why is faithful actions called faithful and who first called it faithful?

Definition: An action $$G$$ on $$X$$ is faithful when $${g_1 \neq g_2 \Rightarrow g_1 x \neq g_2 x}$$ for some $${x \in X}$$ (different elements of $$G$$ act differently at some point).

• good question (+$1$); I always remembered faithful as reliable that no two group elements act the same on all set elements, otherwise there wouldn't be a reason to have two different group elements in the context of their action, but I don't really know – J. W. Tanner Apr 27 at 20:24
• +1: good question, but you might do better on hsm.stackexchange.com – Rob Arthan Apr 27 at 21:51
• Now posted to MO, mathoverflow.net/questions/359121/… – Gerry Myerson May 2 at 1:34